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Trigonometric identities provide a foundation that enables quick solutions to multiple mathematical expressions. This exercise demonstrates applying basic trigonometric ratios of sine, cosine and tangent when performing standard identity simplifications and verifications. The linkage among different trigonometric functions becomes possible through these identities, which enable us to show complex expressions in separate steps. Learning trigonometric connections helps students develop their logical reasoning skills, leading to advanced trigonometric abilities needed for engineering, architecture and physical science fields.
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Exercise 8.3 in the NCERT Solutions for Class 10 presents three important identities which state \(\sin^2 \theta + \cos^2 \theta = 1\) alongside \(1 + \tan^2 \theta = \sec^2 \theta\) and \(1 + \cot^2 \theta = \csc^2 \theta\). The relationships teach students methods to simplify problems through systematic verification of given expressions. The exercise functions as an essential tool for solidifying the knowledge described in NCERT Books. This exercise represents a fundamental requirement for solving trigonometric problems, which progress into height and distance calculations and advanced mathematical concepts.
Q 1: Express the trigonometric ratios
Answer:
We know that
(i)
(ii) We know the identity of
(iii)
Q 3: Choose the correct option. Justify your choice
(A) 1 (B) 9 (C) 8 (D) 0
Answer:
The correct option is (B) = 9
And it is known that
Therefore, equation (i) becomes,
Q 3: Choose the correct option. Justify your choice
(A) 0 (B) 1 (C) 2 (D) –1
Answer:
The correct option is (C)
we can write his above equation as;
Q 3: Choose the correct option. Justify your choice
Answer:
The correct option is (D)
The above equation can be written as;
We know that
therefore,
Answer:
We need to prove-
Now, taking LHS,
LHS = RHS
Hence proved.
Answer:
We need to prove-
Taking LHS;
= RHS
Hence proved.
[ Hint: Write the expression in terms of
Answer:
We need to prove-
Taking LHS;
By using the identity a 3 - b 3 =(a - b) (a 2 + b 2 +ab)
= RHS
Hence proved.
[ Hint : Simplify LHS and RHS separately]
Answer:
We need to prove-
Taking LHS;
Taking RHS;
We know that identity
LHS = RHS
Hence proved.
Answer:
We need to prove -
Dividing the numerator and denominator by
Hence Proved.
Answer:
We need to prove -
Taking LHS;
By rationalising the denominator, we get;
Hence proved.
Q 4: Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
Answer:
We need to prove -
Taking LHS;
[we know the identity
Hence proved.
Answer:
Given the equation,
Taking LHS;
[since
Hence proved
[ Hint : Simplify LHS and RHS separately]
Answer:
We need to prove-
Taking LHS;
Taking RHS;
LHS = RHS
Hence proved.
Answer:
We need to prove,
Taking LHS;
Taking RHS;
LHS = RHS
Hence proved.
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1. Understanding basic trigonometric identities: You must learn the essential three trigonometric identities and understand their value for problem simplification and solution.
2. Verifying trigonometric identities: Perform proofs which establish two sides of an equation to be equal by using proper transformations in combination with trigonometric relations.
3. Developing logical and proof-solving skills: Step-by-step logical verification belongs to the set of skills that students need to develop for checking identities and producing mathematical proofs.
4. Preparing for advanced applications: Construct a strong foundation to solve problems utilising height-distance relationships alongside trigonometric equation methods, as well as actual angle measurement scenarios.
Check Out-
Students must check the NCERT solutions for class 10 of the Mathematics and Science Subjects.
Students must check the NCERT Exemplar solutions for class 10 of the Mathematics and Science Subjects.
Frequently Asked Questions (FAQs)
No, calculators are not allowed in Class 10 board exams, so you must rely on your memorised values and identities.
Yes, Exercise 8.3 is very important as identity-based questions frequently appear in CBSE Class 10 board exams
You should at least remember the fundamental identities and standard angle values to solve Exercise 8.3 effectively.
On Question asked by student community
Hello,
Yes, you can give the CBSE board exam in 2027.
If your date of birth is 25.05.2013, then in 2027 you will be around 14 years old, which is the right age for Class 10 as per CBSE rules. So, there is no problem.
Hope it helps !
Hello! If you selected “None” while creating your APAAR ID and forgot to mention CBSE as your institution, it may cause issues later when linking your academic records or applying for exams and scholarships that require school details. It’s important that your APAAR ID correctly reflects your institution to avoid verification problems. You should log in to the portal and update your profile to select CBSE as your school. If the system doesn’t allow editing, contact your school’s administration or the APAAR support team immediately so they can correct it for you.
Hello Aspirant,
Here's how you can find it:
School ID Card: Your registration number is often printed on your school ID card.
Admit Card (Hall Ticket): If you've received your board exam admit card, the registration number will be prominently displayed on it. This is the most reliable place to find it for board exams.
School Records/Office: The easiest and most reliable way is to contact your school office or your class teacher. They have access to all your official records and can provide you with your registration number.
Previous Mark Sheets/Certificates: If you have any previous official documents from your school or board (like a Class 9 report card that might have a student ID or registration number that carries over), you can check those.
Your school is the best place to get this information.
Hello,
It appears you are asking if you can fill out a form after passing your 10th grade examination in the 2024-2025 academic session.
The answer depends on what form you are referring to. Some forms might be for courses or examinations where passing 10th grade is a prerequisite or an eligibility criteria, such as applying for further education or specific entrance exams. Other forms might be related to other purposes, like applying for a job, which may also have age and educational requirements.
For example, if you are looking to apply for JEE Main 2025 (a competitive exam in India), having passed class 12 or appearing for it in 2025 are mentioned as eligibility criteria.
Let me know if you need imformation about any exam eligibility criteria.
good wishes for your future!!
Hello Aspirant,
"Real papers" for CBSE board exams are the previous year's question papers . You can find these, along with sample papers and their marking schemes , on the official CBSE Academic website (cbseacademic.nic.in).
For notes , refer to NCERT textbooks as they are the primary source for CBSE exams. Many educational websites also provide chapter-wise revision notes and study material that align with the NCERT syllabus. Focus on practicing previous papers and understanding concepts thoroughly.
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